# Talk:Premetric space

## Prametric or premetric

Claim 1. There is a standard terminology for every obscure subset of the axioms for a metric.

Claim 2. "Prametric" is a term used by English-speaking mathematicians.

I have already renamed praclosure operator to preclosure operator. This was an easy case, because the notion of a preclosure operator seems to be relatively standard. This case is more problematic. In fact, while all references for prametric that I found using Google were derived from this article (I have not checked the book yet, which may have had a poor translation), is for what is called a "pseudometric" in this article.

Aleksandr I Akovlevich Khelemskiĭ, A. Ia Khelemskii, A. Ya. Helemskii: Lectures And Exercises on Functional Analysis, p. 14. (Found on books.google.com.)

To make matters worse, the authors of that book even suggest that "quasimetric" is another synonym for what this article calls "pseudometric", which would conflict with our article quasimetric space. Here is another source:

Elliott Pearl: Open Problems in Topology II

For Pearl a "premetric" is what this article calls a "hemimetric", except Pearl allows d(x,y) to be infinity.

I feel very strongly that Wikipedia is not the place to add another weakening presyllable to the current zoo consisting of pre-, para-, quasi-, pseudo-, semi-, hemi- (and probably some more). Especially not one that seems to have no etymology and can easily be confused with pre-. Wikipedia should also not give the impression that there is a standard terminology where in fact there is chaos. This does not rule out supporting serious attempts at standardization, but as far as I can tell there is none.

Unfortunately I do not see an easy way to solve these problems. Any ideas? --Hans Adler 14:09, 15 November 2007 (UTC)

An after-thought: The notions pseudometric and quasimetric seem to be pretty standard. Some people use "pseudo-quasi-metric" or "quasi-pseudo-metric" for what the article calls "hemimetric". This is much clearer, and it cannot be confused with "semimetric". Along with a reasonable standard notion for what the article calls "semimetric" there would be an obvious solution to the problem. --Hans Adler 14:33, 15 November 2007 (UTC)

I'm thinking, the problem is that "prametric" is an easy typo for "parametric": puncturing a vowel is a more common typo than puncturing a consonant, and a single puncture in a longish word is a small difference already. So I would be averse to adopting this term myself. Pete St.John 19:34, 15 November 2007 (UTC)